Mamdani-Larsen fuzzy system based on expectation maximization algorithm and its applications to time series prediction

This work explores how Epanechnikov mixture model can be translated to Mamdani-Larsen fuzzy model. The mathematical equivalence between the conditional mean of an Epanechnikov mixture model and the defuzzified output of a Mamdani-Larsen fuzzy model is proved. The result provides a new perspective of studying the Mamdani-Larsen fuzzy model by interpreting a fuzzy system from a probabilistic viewpoint. Instead of estimating the parameters of the fuzzy rules directly, the parameters of an Epanechnikov mixture model can be firstly estimated using any popular density estimation algorithm, such as expectation maximization. Mamdani-Larsen fuzzy model trained in the new way has higher accuracy and stronger anti-noise capability. After comparing the simulation results with the ones obtained from other fuzzy system modeling tools, it can be claimed that the results are successful.